Let me start off by saying the book I am looking for is not ‘The Secret Garden’ by Burnett, and is not ‘Secret Friend’ by Marilyn Sachs.  I’ve also considered but tossed out ‘Mystery Back of the Mountain’by Mary C Jane, although I think that’s the closest I ever got to a eureka moment but I don’t recall a male companion in the story.

Read the book in 4th grade, 1982, it was about 1″ in thickness,  it was a hard cover, fabric, pale sage green. It didn’t seem new.
I recall a “W” on the spine of the book. In the author’s name perhaps?
I do not recall pictures, but that doesn’t mean there were none, just that this was a children’s novel, not a little kid’s book.
The title included words like Secret, Friend, Mysterious Friend, Garden ?…
The main character was a young girl, 10-12 years old possibly.
The book has the dark English feel to it similar to The Secret Garden. I recall grassy hills, gardens, whispers, not modern.
The biggest memory in the book is the main girl character meeting a mysterious girl named Olivia (which makes finding this on Google impossible due to the pig of the same name) and becoming friends with her.
This is why I don’t think that it’s Mystery Back of the Moutain, because I don’t recall a male character tagging along in their friendship but I might be wrong.
My other last ditch guess is “THE HOUSE OF SECRETS” aka “The Secret Passage” by Nina Bawden.  Is there an OLIVIA in that book? This book however, also contains a male child that I don’t recall.
Would love to find this so I can pass it on to my daughter 🙂